The Lakshmanan–Porsezian–Daniel model with arbitrary refractive index and its solution

Abstract

The generalized Lakshmanan–Porsezian–Daniel model with arbitrary refractive index is considered. The main problem that is solved for this nonlinear partial differential equation is the existence of exact solutions in the form of periodic and solitary waves. It is shown that for an arbitrary refractive index of the equation, there are solutions in the form of solitary waves corresponding to optical solitons. For the classical case of the Lakshmanan–Porsezian–Daniel equation at n=1 and for new case at n=12 the equation has a solution in the form of periodic waves. These exact solutions are expressed via the Jacobi and the Weierstrass elliptic functions.